Is the language ${L}_{n}$ regular?

[JamesBwoii]

Hi, I'm back with another question, but the opposite of last time.

The question is:

For each positive integer $n$, let ${L}_{n}$ = { ${a}^{k}$ $|$ $k$ is a multiple of $n$ }
Show that for each $n$ the language ${L}_{n}$ is regular. As far as I understand you cannot use pumping lemma to prove a language is regular.

I assume that leaves me with having to do a NFA, DFA or regular expression as I don't know where to begin to create one of those for this language.

Thanks!

 

[Evgeny.Makarov]

The easiest way to define regular languages is using regular expressions. Can you write a regular expression describing $L_1=\{a^k\mid k\ge0\}=\{a\}^*$?

 

[JamesBwoii]

The easiest way to define regular languages is using regular expressions. Can you write a regular expression describing $L_1=\{a^k\mid k\ge0\}=\{a\}^*$?

Honestly no, I just can't see it. I'm really struggling with this particular problem sheet.

 

[Evgeny.Makarov]

Then you should read the definition and examples of regular expressions, for example, in Wikipedia.